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A biconvex thin lens is prepared from gl...

A biconvex thin lens is prepared from glass of refractive index `3//2.` The two bounding surfaces have equal radii of `25cm` each. One of the surfaces is silvered from outside to make it reflecting. Where should an object be placed before this lens so that the image coincides with the object.

Text Solution

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The correct Answer is:
A, B, C
Equivalent focal length of this system which behaves like a mirror is given `rarr+ve`
by
`1/f=(2(mu_2//mu_1))/(R_2)-(2(mu_2//mu_1-1))/(R_1)`
Here, `R_1=+25 cm, R_2=-25 cm, mu_1=1`
and `mu_2=3//2`
Image coincides with object, hence, `u=v=-x(say)`
Substituting in mirror formula, we have
`1/-x-1/x=(2(3//2))/(-25)-(2(3//2))/(25)`
or `2/x=3/25+1/25=4/25`
`:. x=12.5 cm`
Hence, the object should be placed at a distance `12.5 cm` in front of the silvered lens.
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